A study of scaling physics in a Polywell device

Abstract

The Polywell is an Inertial Electrostatic Confinement (IEC) device that aims to confine ions at fusion energies. The Polywell uses a virtual cathode in place of a metal grid cathode used in regular IEC devices, in which a high voltage is applied to the grid to accelerate ions to fusion energies and confine them in a spherical geometry. The virtual cathode is produced by confining high energy electrons in a magnetic well by mirror reflections, which produces a potential well. Three orthogonal pairs of coils with antiparallel currents are placed equidistant from the centre of the device, such that the six coils make up the faces of a cube. In this way a magnetic well is produced with a magnetic null at the centre of the device and strong magnetic fields near the coils. Spherically symmetric potential wells are also required in order to maximise the degree of ion focusing attained in the core of the device. The formation of deep, symmetrical potential wells is critical to the functioning of the Polywell and is the major focus of this thesis. This thesis aims to explore how the depth and symmetry of potential wells vary with a number of device parameters. These include injected electron current and electron energy and magnetic field strength. The spacing of magnetic field coils is also investigated. Varying the spacing of the magnetic field coils changes the relative magnetic field strength in the different cusps of the device and hence the electron trapping in these cusps. Electron losses through the cusps represent a major energy loss mechanism and are a major impediment to the potential of the device to eventually reach net fusion energy. The electron trapping is maximised by determining the ideal intercoil spacing. Different sizes of magnetic field coil were used to investigate how increasing the device size improves the electron trapping and potential well formation. It is hypothesized that larger devices are able to trap higher energy electrons and produce deeper potential wells capable of accelerating ions to fusion energies. The scaling experiments with smaller devices are used to estimate the size of device needed to reach fusion energies. In order to investigate the potential formation multiple secondary electron emission capacitive probes (SECP) were constructed. The use of these probes in the Polywell plasma could give a direct measure of the plasma potential and hence the potential well. However, this type of probe has not be shown to be effective in the highly magnetised non-Maxwellian, non-neutral electron plasma found in the Polywell. A planar vacuum diode within a Helmholtz pair is used to test the applicability of a SECP in such a plasma, with magnetic fields up to 0.35 T, and for electron energies of 100 eV-4000 eV. The plasma potential is accurately measured by the probe when the electron Larmor radius is greater than the probe diameter. When the electron Larmor radius is less than the probe diameter, the measured plasma potential is underestimated. However, this effect ceases at a finite Larmor radius and the SECP can be used to measure the plasma potential in high magnetic fields using a correction factor. A small Polywell with a 48 mm average coil diameter is tested with central face magnetic fields up to 0:5 T. The effect of magnetic field coil current and electron injection current and electron energy on the development of potential wells is observed. The electron emission current is varied from 150- 1680 mA and electron energies range between 150-800 V. These device parameters are tested over a much larger range than previously examined. A linear relationship is observed between potential well depth and injection current. A non-linear relationship is observed between potential well depth and magnetic field strength, with further increases to the magnetic field strength having less effect on the well depth. Investigations are made into the effect of the applied magnetic field current on the amount of emitted electrons that are injected into the device. An analytical model is created to estimate the electron confinement time from the measured potential well depth. From these results, an experimentally derived equation for electron confinement time is constructed, based on the experimental parameters of electron energy and coil current. These results are compared to a similar equation derived from a particle orbit simulation. A similar setup is used to again test the effect of magnetic field strength and emission current on the potential well depth. However, in the second experiment the two variables are completely decoupled. A nonlinear relationship is now observed between emission current and potential well depth, with the increases to both variables having diminishing returns on the well depth achieved. Electron energies of 200-800 V were used with emission currents of 3-190 mA. More accurate electron emission currents were performed in this experiment. The intercoil spacing is varied to determine the effect of changing the relative magnetic field at the face, corner, and edge cusps of the device. Multiple capacitive probes are used in these cusp locations and at the centre of the device. The use of multiple probes allows the spherical symmetry of the potential wells and the relative electron trapping at the different device cusps to be determined. The effect of a hydrogen background gas on the potential well formation and as a possible source of fuel ions in a fusion capable Polywell is investigated. Three pressures of 0.1 mTorr, 1 mTorr and 10 mTorr, in addition to measurements at a base pressure of 0.007 mTorr were used. The effect of device scaling is explored by increasing the coil size to an average diameter of 77.5 mm. Based on these results, a geometric progression is used to determine the size of a device needed to reach fusion energies. Two different types of coil housing are used, which demonstrates how the conformal nature of the coil housing to the magnetic fields affect potential well formation. Electron confinement time estimations are made for device configurations that produced reasonably spherically symmetric potential wells. As these estimations rely on a spherical well assumption and the measured injection current, they are thought to be more accurate than those found in the first experiment.